Multi-products Location-Routing Problem with Pickup and Delivery

An extended variant of Location-Routing Problem namely LRP with Multi-Product and Pickup and Delivery (LRPMPPD) is considered in this study. The proposed model deals with simultaneously selecting (locating) one or more facilities from a set of potential hub (locations), assigning customers to the selected hubs and defining routes of the vehicles for serving multi-product customers demand in such way that each selected hub must be visited once for delivering, though they can be visited many times for picking up. We propose a mixed integer linear programming formulation and a heuristic approach for this problem. Since there is not any instance compatible with LRP-MPPD in the literature, we have extended known LRP instances to evaluate the performance of the proposed approach. A comparison with CPLEX shows that the proposed algorithm is a viable approach to solve small and large size LRP-MPPD instances.